# How to determine the distribution a dataset follows without plotting or visualizing it?

I am given a data set of 100k instances and I am being told that it belongs to one of four statistical distributions (normal, truncated normal, poisson and uniform). I am wondering how I may go about finding which stastical model best represents this dataset perhaps using numpy?

What I am thinking is to literally count occurrences of every instance and then divide over size giving the probability of each instance, and then attempting to find that probability using different statistical models such as P(X) = 1/b-a for uniform and see which one it best matches? I feel like this is very tedious and will not work.

Can anyone guide me in the right direction?

• Why can you not visualize or plot? Feb 4, 2019 at 3:31
• Maybe a $\chi^2$ goodness of fit test. Feb 4, 2019 at 7:50
• It's not possible to distinguish a Normal distribution from a truncated Normal using any amount of data, because the truncation point could be extreme. (It is possible, however, to determine that the data may be truncated Normal but definitely are not Normal.) Given the basic and obvious qualitative differences among the Normal, Poisson, and Uniform families, even the most primitive plot or test with 100K values ought to perform well unless the Poisson parameter is huge.
– whuber
Feb 4, 2019 at 14:37
• Can you elaborate on the above point? What sort of "tests" can one use? I can't plot because it is a requirement for one of my assignments. Feb 4, 2019 at 18:15